A space optic instrument or a space telescope comprises an optical focusing system generally comprising several mirrors and an image analysis device comprising photoreception means and computing means making it possible to ensure the processing of the images received. The photoreception means can be either a matrix of photoreceptors, or an assembly comprising one or more rows of photoreceptor arrays. In this case, the instrument comprises opto-mechanical means ensuring the scanning of the image.
Whatever the configuration employed, it is clear that one seeks to obtain the most precise possible images. Now, optic instruments are capable only of measuring a luminous intensity and the image phase information is therefore lost. For example, in a scanning optical system, the data acquired in the direction x of the rows of arrays and denoted {d(x)} are noisy measurements of the convolution of the object observed, written o(x,λ) at a wavelength λ, with the percussional response of the optical system or “PSF”, the acronym standing for “Point Spread Function”, and denoted h(x,λ), integrated over the spectral band of intensity f(λ) of the acquisition pathway.
We thus have relation 1:
                              d          ⁡                      (            x            )                          =                              N            ⁡                          [                              h                *                                  o                  ⁡                                      (                    x                    )                                                              ]                                =                      N            ⁡                          [                                                ∫                  λ                                ⁢                                                      (                                                                  h                        ⁡                                                  (                                                      x                            ,                            λ                                                    )                                                                    *                                              o                        ⁡                                                  (                                                      x                            ,                            λ                                                    )                                                                                      )                                    ⁢                                      f                    ⁡                                          (                      λ                      )                                                        ⁢                                      ⅆ                    λ                                                              ]                                                          Relation        ⁢                                  ⁢        1            
The optical quality of the instrument is characterized by a phase error of the wavefront, also called the “WFE”, the acronym standing for “Wave-Front Error”. This WFE takes into account the aberrations of the mirrors of the telescope, and also the various defects of alignment of the mirrors constituting the telescope or of the detector with respect to the telescope. The WFE information is “contained” in the optical PSF of the system denoted hOPT(x,λ), the global PSF being equal to the convolution of the latter with other components related to the quality of the detector, to movements, etc. We thus have relation 2:
                                          h            OPT                    ⁡                      (                          x              ,              λ                        )                          =                                                                                          TF                                      -                    1                                                  ⁡                                  [                                                            A                      ⁡                                              (                        p                        )                                                              ⁢                                          ⅇ                                              ⅈ                        ⁢                                                                                                  ⁢                                                  φ                          ⁡                                                      (                                                          p                              ,                              λ                                                        )                                                                                                                                ]                                            ⁢                              (                                  x                                      λ                    ⁢                                                                                  ⁢                    F                                                  )                                                          2                                    Relation        ⁢                                  ⁢        2            where A(p) and φ(p,λ) are respectively the amplitude and the phase of the field at the level of the pupil of the instrument, F being the focal length of the instrument.
An estimation of the WFE is essential in so far as its knowledge makes it possible to correct all or part of the defects of the instrument so as to retrieve as clean an image as possible of the object. It requires the deployment of a dedicated device. This knowledge is indispensable when the instrument is active, that is to say it possesses means making it possible to correct the shape or the alignment of the mirrors so as to constantly retain as sharp as possible an image.
There exist various wavefront analysis solutions making it possible to retrieve the WFE. Generally, analysers are classed into two families, namely so-called “pupil plane” analysers and so-called “focal plane” analysers.
Among pupil plane analysers will mainly be noted the Shack-Hartmann method which consists in sampling the entrance pupil and in imaging in a dedicated pathway all of the observed scenes, so as to measure the WFE locally. The drawback of such an approach is the use of a part of the entrance flux for an “ancillary” analysis pathway, as well as the complexity of the optical device to be deployed.
Focal plane analysers do not have any such drawbacks, since they consist in using acquisitions carried out at the level of the focal plane of the instrument to estimate the wavefront. One way of treating this problem is, for example, to acquire two images of the same scene o(x), one being defocused with respect to the other and to use an algorithm of phase diversity type. Phase diversity can be used for image restoration purposes, the aim is then to find o(x), or for wavefront analysis purposes, the aim is in this case to find the WFE φ(p), the WFE generally being parametrized as a linear combination of Zernike vectors representative of the focusing defect or of geometric aberrations such as astigmatism.
Analyses using phase diversity therefore make it possible to determine the WFE of the telescope on the basis of image acquisitions. This phase information can be used in an active optic system to correct it in closed-loop, or else a posteriori to restore the acquired data and thus improve the image quality.
A great many articles have been published, over nearly 30 years, on wavefront analysis using phase diversity and space applications of this analysis. The great majority propose diverse algorithmic approaches for solving this problem, others describe its application to particular goals when the object is known and pointlike. One then speaks of phase retrieval.
Mention will be made notably of the article by Gonsalves entitled “Phase retrieval and diversity in adaptive optics”, Optical Engineering, 21, 1982 which is considered to be the seminal article on phase diversity.
Mention will also be made of the article by Paxman entitled “Joint estimation of object and aberrations by using phase diversity”, Journal of the Optical Society of America A, 9(7), 1992 which makes reference to and which presents the most commonly used algorithmic approach.
Mention will be made also of the article by Fienup entitled “Hubble space telescope characterized by using phase retrieval algorithms”, Applied Optics, 32(10):1747-1767, 1993; that by Löfdahl entitled “Wavefront sensing and image restoration from focused and defocused solar images”, Astronomy and Astrophysics, 107:243-264, 1994 and finally that by Dean entitled “Phase retrieval algorithm for JWST flight testbed telescope, Space telescopes and Instrumentation”, SPIE 6265, 2006 which present applications of phase diversity to concrete cases such as the study of sunspots, the adjustment of the Hubble telescope or “HST” for Hubble Space Telescope or that of the “JWST” (“James Webb Space Telescope”) telescope.
The article by Kendrick entitled “Closed-loop wavefront correction using phase diversity”, SPIE 3356 Space Telescopes and Instruments, 1998 describes a closed-loop approach, with a few architectural designs of phase diversity sensors.
Finally, the article by Luke entitled “Optical wavefront reconstruction: theory and numerical methods”, SIAM review 44(2):169-224, 2002 presents a state of the art of the various algorithmic approaches.
Patents have also been filed on wavefront analysis either on the phase diversity algorithm, or on the means of simply creating the defocusings required by this phase diversity algorithm.
Mention will be made notably of U.S. Pat. No. 4,309,602 entitled “Wavefront sensing by phase retrieval” which describes the algorithmic approach and the framework of the use of a sensor-wavefront analysis-adaptive optics loop.
Mention will also be made of U.S. Pat. No. 5,598,261 entitled “Wavefront sensor for a scanning imager” which presents a concept using “TDI” for “Time Delay Integration” comprising two parallel detectors, the second one being defocused with respect to the first by the provision of a transparent substrate. This may involve defocusings added over all or some of the length of the detector or else at the level of inter-array zones.
Mention will also be made of U.S. Pat. No. 5,610,707 entitled “Wavefront sensor for a staring imager” which presents a concept similar to the above but adapted to a matrix sensor with use of a beam splitter to obtain the focused and defocused images.
Mention will be made of application US 2004/0099787A1 entitled “System and method for determining optical aberrations in scanning imaging systems by phase diversity” which presents a concept using TDI comprising two parallel detector rows, one thereof, potentially composed of several elements, being shifted along the optical axis with respect to the other so as to defocus the image.
Patents US 2004/0056174 entitled “Fast phase diversity wavefront correction using a neural network” and FR 2919052 entitled “Method for estimating at least one deformation of the wavefront of an optical system or of an object observed by the optical system and associated device” present an adaptation of the algorithmic part for fast-calculation requirements.
Finally, U.S. Pat. No. 7,274,442 entitled “Closed loop wavefront sensor using field programmable gate array” presents an architectural approach of the onboard algorithmic processing, combining the use of phase diversity sensors and FPGAs.